Answer
455.7k+ views
Hint: - Here, we use bisector formulas to find midpoints.
Let \[{\text{A(}} - {\text{6,8)}}\] and \[{\text{B(8,}} - {\text{6)}}\] and \[{\text{P,Q,R}}\] divides \[{\text{AB}}\] in four equal parts \[{\text{Q}}\] divides \[{\text{AB}}\] in \[{\text{1:1}}\],so \[{\text{Q}}\] is the midpoint of \[{\text{AB}}\].
So coordinates of \[{\text{Q}}\] are \[\dfrac{{ - {\text{6 + 8}}}}{2}{\text{,}}\dfrac{{{\text{8}} - {\text{6}}}}{2}\]
\[ \Rightarrow {\text{Q}}(1,1)\]
Similarly ${\text{P}}$ is the midpoint of \[{\text{AQ}}\]
So coordinates of ${\text{P }}$ are \[\dfrac{{ - {\text{6 + 1}}}}{2},\dfrac{{8+1}}{2}\]
\[ \Rightarrow {\text{P}}\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right)\]
And now \[{\text{R }}\] is the midpoint of ${\text{QB}}$
So coordinates of \[{\text{R}}\] are \[\dfrac{{1 + 8}}{2},\dfrac{{1 - 6}}{2}\]
\[ \Rightarrow {\text{R }}\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]
The points which divide the line in four equal parts are \[\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right);(1,1);\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]
Note:-Whenever we face such types of questions it is better to denote the coordinate by letter and then bisect the first line and after that bisect that line. Which are made by the bisector of the first line.
![seo images](https://www.vedantu.com/question-sets/0356902c-6e9e-49c8-8753-026ce637c28e3616158134145650901.png)
Let \[{\text{A(}} - {\text{6,8)}}\] and \[{\text{B(8,}} - {\text{6)}}\] and \[{\text{P,Q,R}}\] divides \[{\text{AB}}\] in four equal parts \[{\text{Q}}\] divides \[{\text{AB}}\] in \[{\text{1:1}}\],so \[{\text{Q}}\] is the midpoint of \[{\text{AB}}\].
So coordinates of \[{\text{Q}}\] are \[\dfrac{{ - {\text{6 + 8}}}}{2}{\text{,}}\dfrac{{{\text{8}} - {\text{6}}}}{2}\]
\[ \Rightarrow {\text{Q}}(1,1)\]
Similarly ${\text{P}}$ is the midpoint of \[{\text{AQ}}\]
So coordinates of ${\text{P }}$ are \[\dfrac{{ - {\text{6 + 1}}}}{2},\dfrac{{8+1}}{2}\]
\[ \Rightarrow {\text{P}}\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right)\]
And now \[{\text{R }}\] is the midpoint of ${\text{QB}}$
So coordinates of \[{\text{R}}\] are \[\dfrac{{1 + 8}}{2},\dfrac{{1 - 6}}{2}\]
\[ \Rightarrow {\text{R }}\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]
The points which divide the line in four equal parts are \[\left( { - \dfrac{5}{2},\dfrac{9}{2}} \right);(1,1);\left( {\dfrac{9}{2},\dfrac{{ - 5}}{2}} \right)\]
Note:-Whenever we face such types of questions it is better to denote the coordinate by letter and then bisect the first line and after that bisect that line. Which are made by the bisector of the first line.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)